To Kill A Mockingbird Using Swarm Intelligence Examples
Ant Colony Optimization
EDWIN WONG PHILLIP SUMMERS ROSALYN KU PATRICK XIE PIC 10C SPRING 2011
Swarm Intelligence
Swarms
Swarm of bees Ant colony as swarm of ants Flock of birds as swarm of birds Traffic as swarm of cars Immune system as swarm of cells and molecules ...
Swarm Intelligence/Agent Based Modeling
Model complex behavior using simple agents
Swarm Intelligence
Digital Crumbs a la Hansel and Gretel
Idea: stigmergy is a mechanism of communication by modifying the environment Example
Take some dirt in your mouth Moisten it with pheromones Walk in the direction of the strongest pheromone concentration Drop what you are carrying where the smell is the strongest
Ant Colony Optimization uses artificial stigmergy
Swarm Intelligence
Ant Colony Optimization
Marco Dorigo (1991) – …show more content…
PhD thesis
Technique for solving problems which can be expressed as finding good paths through graphs Each ant tries to find a route between its nest and a food source
Swarm Intelligence
The behavior of each ant in nature
Wander randomly at first, laying down a pheromone trail If food is found, return to the nest laying down a pheromone trail If pheromone is found, with some increased probability follow the pheromone trail Once back at the nest, go out again in search of food
However, pheromones evaporate over time, such that unless they are reinforced by more ants, the pheromones will disappear.
Ant Colony Optimization
1. The first ant wanders randomly until it finds the food
source (F), then it returns to the nest (N), laying a pheromone trail
Ant Colony Optimization
2.
3.
Other ants follow one of the paths at random, also laying pheromone trails. Since the ants on the shortest path lay pheromone trails faster, this path gets reinforced with more pheromone, making it more appealing to future ants. The ants become increasingly likely to follow the shortest path since it is constantly reinforced with a larger amount of pheromones. The pheromone trails of the longer paths evaporate.
Ant Colony Optimization
Paradigm for optimization problems that can be expressed as finding short paths in a graph
Goal
To design technical systems for optimization, and NOT to design an accurate model of nature
Ant Colony Optimization
Nature Natural habitat Nest and food Ants Visibility Pheromones Foraging behavior Computer Science Graph (nodes and edges) Nodes in the graph: start and destination Agents, our artificial ants The reciprocal of distance, η Artificial pheromones ,τ Random walk through graph (guided by pheromones)
Ant Colony Optimization
Scheme:
Construct ant solutions Define attractiveness τ, based on experience from previous solutions Define specific visibility function, η, for a given problem (e.g. distance)
Ant walk
Initialize ants and nodes (states) Choose next edge probabilistically according to the attractiveness and visibility
Each ant maintains a tabu list of infeasible transitions for that iteration Update attractiveness of an edge according to the number of ants that pass through
Ant Colony Optimization
Pheromone update
Parameter is called evaporation rate Pheromones = long-term memory of an ant colony ρ small ρ large low evaporation high evaporation slow adaptation fast adaptation
Note: rules are probabilistic, so mistakes can be made! “new pheromone” or Δτ usually contains the base attractiveness constant Q and a factor that you want to optimize
(e.g. ) Q/length of tour
General Ant Colony Pseudo Code
Initialize the base attractiveness, τ, and visibility, η, for each edge; for i < IterationMax do: for each ant do: choose probabilistically (based on previous equation) the next state to move into;
add that move to the tabu list for each ant; repeat until each ant completed a solution; end; for each ant that completed a solution do: update attractiveness τ for each edge that the ant traversed; end; if (local best solution better than global solution) save local best solution as global solution; end; end;
Heuristic Information
Heuristics refers to experience-based techniques for problem solving, learning, and discovery Prime example: trial and error In computer science, metaheuristic is a computational method that optimizes a problem by iteratively trying to improve a candidate solution
Example: black box, cracking a combination lock, planning a route from Miami to Dallas
Metaheuristics allows us to find the best solution over a discrete search-space
Traveling Salesman Problem
Traveling Salesman Problem (TSP)
In the Traveling Salesman Problem (TSP) a salesman visits n cities once. Problem: What is the shortest possible route?
Solutions?
Brute Force Method:
Create permutations for all N cities within the TSP Iteratively check all distances Can you guys figure out the Big O notation for such a problem?
Greedy Algorithm:
Searches for locally optimal solutions
ACO and the Traveling Salesman Problem
An artificial ant k has a memory of the cities that it has already visited, Mk or tabu Add heuristic information to ant walk: τ(e) describes the attractiveness of an edge η(e) = 1/d inverse distance (visibility) between cities
An ant k in city i chooses the next city according to
ACO and the Traveling Salesman Problem
e’ is an edge that the ant hasn’t visited α and β balance impact of pheromone vs. visibility (both commonly fixed at 1) favors edges which are shorter and have more pheromone τ is the amount of pheromone on the edge (i,j) τ = (1- ρ) * τ + Δτk Δτk = Q/Lk , Q is constant, Lk is the length of tour of ant k
Ant System Algorithm for TSP
Pseudocode: initialize all edges to (small) initial pheromone level τ0; place each ant on a randomly chosen city; for each iteration do: do while each ant has not completed its tour: for each ant do: move ant to next city by the probability function end; end; for each ant with a complete tour do: evaporate pheromones; apply pheromone update; if (ant k’s tour is shorter than the global solution) update global solution to ant k’s tour end; end;
Benefits of Ant Colony Optimization
Can solve certain NP-Hard problems in Polynomial time Directed-Random Search
Allows a balance between using previous knowledge and exploring new solutions
Positive feedback for good solutions/Negative feedback for bad solutions Approximately convergent Optimal if not absolutely correct solutions In certain examples of ACO, no one “ant” is required to actually complete an accurate solution
Some Observed Problems
Problem specific
Limited to problems that can be simulated by graphs and optimized Coding difficulties for different problems
Ineffective utilization of previously acquired information, specifically the global solution Depending on the design of the algorithm, it can converge towards a (less optimal) solution.
Improvements
We might like to add factors to minimize the time it takes to reach an acceptable solution. Use the elements of previous solutions
This allows for faster convergence As we construct more and more solutions, there is more information available about the probable “right” choices to make
The decision making process might weigh exploration vs. heuristic value
Versions of Ant Colony
Ant System: what we just went over Ant Colony System:
Pseudo-random proportion rule: at each decision point for an ant, it has a probability (1-q0) of using the same probability function as in the Ant System or q0 of picking the best next node based on previous solutions
Versions of Ant Colony
Global Trail Update: only the best solution since the start of the computation will globally update its pheromones Local Trail Update: all ants consume/decrease pheromones along the path that they travel
Elitist Ant System:
Both the global solution and each ant update their edges with pheromones on each iteration
Applications
Applications
Routing problems Urban transportation systems Facility placement Scheduling problems
How can we modify the algorithm?
Vary the importance of pheromone Play around with evaporation rate Add time constraint Add obstacles
Applications
Urban solid waste collection
Traffic flow optimization
To sum it up:
General paradigm for optimization problems Inspiration from nature, but with smarter agents Paths found by ant represent solutions for the problem Choice of path influenced by previous experience Pheromones as model of collective memory of a swarm Tunable parameters that affect performance
To see a creative implementation of Ant Colony Optimization, check out Forrest O.’s design: http://www.openprocessing.org/visuals/?visualID=15109
References
Dorigo M, Stützle T. Ant Colony Optimization. MIT Press; 2004 Vittorio Maniezzo, Luca Maria Gambarde, Fabio de Luigi. http://www.cs.unibo.it/bison/publications/ACO.pdf Monash University CSE 460 lecture notes http://www.csse.monash.edu.au/~berndm/CSE460/Lectu res/cse460-9.pdf “Ant colonies for the traveling salesman problem” http://www.idsia.ch/~luca/acs-bio97.pdf
EDWIN WONG PHILLIP SUMMERS ROSALYN KU PATRICK XIE PIC 10C SPRING 2011
Swarm Intelligence
Swarms
Swarm of bees Ant colony as swarm of ants Flock of birds as swarm of birds Traffic as swarm of cars Immune system as swarm of cells and molecules ...
Swarm Intelligence/Agent Based Modeling
Model complex behavior using simple agents
Swarm Intelligence
Digital Crumbs a la Hansel and Gretel
Idea: stigmergy is a mechanism of communication by modifying the environment Example
Take some dirt in your mouth Moisten it with pheromones Walk in the direction of the strongest pheromone concentration Drop what you are carrying where the smell is the strongest
Ant Colony Optimization uses artificial stigmergy
Swarm Intelligence
Ant Colony Optimization
Marco Dorigo (1991) – …show more content…
PhD thesis
Technique for solving problems which can be expressed as finding good paths through graphs Each ant tries to find a route between its nest and a food source
Swarm Intelligence
The behavior of each ant in nature
Wander randomly at first, laying down a pheromone trail If food is found, return to the nest laying down a pheromone trail If pheromone is found, with some increased probability follow the pheromone trail Once back at the nest, go out again in search of food
However, pheromones evaporate over time, such that unless they are reinforced by more ants, the pheromones will disappear.
Ant Colony Optimization
1. The first ant wanders randomly until it finds the food
source (F), then it returns to the nest (N), laying a pheromone trail
Ant Colony Optimization
2.
3.
Other ants follow one of the paths at random, also laying pheromone trails. Since the ants on the shortest path lay pheromone trails faster, this path gets reinforced with more pheromone, making it more appealing to future ants. The ants become increasingly likely to follow the shortest path since it is constantly reinforced with a larger amount of pheromones. The pheromone trails of the longer paths evaporate.
Ant Colony Optimization
Paradigm for optimization problems that can be expressed as finding short paths in a graph
Goal
To design technical systems for optimization, and NOT to design an accurate model of nature
Ant Colony Optimization
Nature Natural habitat Nest and food Ants Visibility Pheromones Foraging behavior Computer Science Graph (nodes and edges) Nodes in the graph: start and destination Agents, our artificial ants The reciprocal of distance, η Artificial pheromones ,τ Random walk through graph (guided by pheromones)
Ant Colony Optimization
Scheme:
Construct ant solutions Define attractiveness τ, based on experience from previous solutions Define specific visibility function, η, for a given problem (e.g. distance)
Ant walk
Initialize ants and nodes (states) Choose next edge probabilistically according to the attractiveness and visibility
Each ant maintains a tabu list of infeasible transitions for that iteration Update attractiveness of an edge according to the number of ants that pass through
Ant Colony Optimization
Pheromone update
Parameter is called evaporation rate Pheromones = long-term memory of an ant colony ρ small ρ large low evaporation high evaporation slow adaptation fast adaptation
Note: rules are probabilistic, so mistakes can be made! “new pheromone” or Δτ usually contains the base attractiveness constant Q and a factor that you want to optimize
(e.g. ) Q/length of tour
General Ant Colony Pseudo Code
Initialize the base attractiveness, τ, and visibility, η, for each edge; for i < IterationMax do: for each ant do: choose probabilistically (based on previous equation) the next state to move into;
add that move to the tabu list for each ant; repeat until each ant completed a solution; end; for each ant that completed a solution do: update attractiveness τ for each edge that the ant traversed; end; if (local best solution better than global solution) save local best solution as global solution; end; end;
Heuristic Information
Heuristics refers to experience-based techniques for problem solving, learning, and discovery Prime example: trial and error In computer science, metaheuristic is a computational method that optimizes a problem by iteratively trying to improve a candidate solution
Example: black box, cracking a combination lock, planning a route from Miami to Dallas
Metaheuristics allows us to find the best solution over a discrete search-space
Traveling Salesman Problem
Traveling Salesman Problem (TSP)
In the Traveling Salesman Problem (TSP) a salesman visits n cities once. Problem: What is the shortest possible route?
Solutions?
Brute Force Method:
Create permutations for all N cities within the TSP Iteratively check all distances Can you guys figure out the Big O notation for such a problem?
Greedy Algorithm:
Searches for locally optimal solutions
ACO and the Traveling Salesman Problem
An artificial ant k has a memory of the cities that it has already visited, Mk or tabu Add heuristic information to ant walk: τ(e) describes the attractiveness of an edge η(e) = 1/d inverse distance (visibility) between cities
An ant k in city i chooses the next city according to
ACO and the Traveling Salesman Problem
e’ is an edge that the ant hasn’t visited α and β balance impact of pheromone vs. visibility (both commonly fixed at 1) favors edges which are shorter and have more pheromone τ is the amount of pheromone on the edge (i,j) τ = (1- ρ) * τ + Δτk Δτk = Q/Lk , Q is constant, Lk is the length of tour of ant k
Ant System Algorithm for TSP
Pseudocode: initialize all edges to (small) initial pheromone level τ0; place each ant on a randomly chosen city; for each iteration do: do while each ant has not completed its tour: for each ant do: move ant to next city by the probability function end; end; for each ant with a complete tour do: evaporate pheromones; apply pheromone update; if (ant k’s tour is shorter than the global solution) update global solution to ant k’s tour end; end;
Benefits of Ant Colony Optimization
Can solve certain NP-Hard problems in Polynomial time Directed-Random Search
Allows a balance between using previous knowledge and exploring new solutions
Positive feedback for good solutions/Negative feedback for bad solutions Approximately convergent Optimal if not absolutely correct solutions In certain examples of ACO, no one “ant” is required to actually complete an accurate solution
Some Observed Problems
Problem specific
Limited to problems that can be simulated by graphs and optimized Coding difficulties for different problems
Ineffective utilization of previously acquired information, specifically the global solution Depending on the design of the algorithm, it can converge towards a (less optimal) solution.
Improvements
We might like to add factors to minimize the time it takes to reach an acceptable solution. Use the elements of previous solutions
This allows for faster convergence As we construct more and more solutions, there is more information available about the probable “right” choices to make
The decision making process might weigh exploration vs. heuristic value
Versions of Ant Colony
Ant System: what we just went over Ant Colony System:
Pseudo-random proportion rule: at each decision point for an ant, it has a probability (1-q0) of using the same probability function as in the Ant System or q0 of picking the best next node based on previous solutions
Versions of Ant Colony
Global Trail Update: only the best solution since the start of the computation will globally update its pheromones Local Trail Update: all ants consume/decrease pheromones along the path that they travel
Elitist Ant System:
Both the global solution and each ant update their edges with pheromones on each iteration
Applications
Applications
Routing problems Urban transportation systems Facility placement Scheduling problems
How can we modify the algorithm?
Vary the importance of pheromone Play around with evaporation rate Add time constraint Add obstacles
Applications
Urban solid waste collection
Traffic flow optimization
To sum it up:
General paradigm for optimization problems Inspiration from nature, but with smarter agents Paths found by ant represent solutions for the problem Choice of path influenced by previous experience Pheromones as model of collective memory of a swarm Tunable parameters that affect performance
To see a creative implementation of Ant Colony Optimization, check out Forrest O.’s design: http://www.openprocessing.org/visuals/?visualID=15109
References
Dorigo M, Stützle T. Ant Colony Optimization. MIT Press; 2004 Vittorio Maniezzo, Luca Maria Gambarde, Fabio de Luigi. http://www.cs.unibo.it/bison/publications/ACO.pdf Monash University CSE 460 lecture notes http://www.csse.monash.edu.au/~berndm/CSE460/Lectu res/cse460-9.pdf “Ant colonies for the traveling salesman problem” http://www.idsia.ch/~luca/acs-bio97.pdf